Question 13.8: Calculate [H^+] in a 0.100 M solution of nitrous acid, HNO2,...

Calculate [H^+] in a 0.100 M solution of nitrous acid, HNO_2, for which K_a = 6.0 \times  10^{-4}.

ANALYSIS

Information given:               [HNO_2]_o (0.100 M);         K_a (6.0 \times  10^{-4})
Asked for:                              [H^+] = [H^+]_{eq}

STRATEGY

1. The table setup is identical to that of Example 13.7 giving the equilibrium expression
Substitute values for equilibrium from the table. K_a = \frac{[H^+][{NO_2}^{-}]}{[HNO_2]} = \frac{(x)(x)}{0.100  –  x}
2. Assume x << 0.100 and solve for x.
3. Check your assumption by calculating % ionization.
4. If the % ionization is less than 5%, your assumption is valid. If not, solve for x using the quadratic equation.